About 7,000 Machinists marched in solidarity at Boeing’s wide-body jet plant in Everett on Friday morning, a large banner, hanging from a balcony, emblazoned with just one word: “Strike!”

Workers at the rally declared their rejection of the company’s Thursday contract offer with chants of “Paint the Lines,” a reference to the green perimeter lines that Boeing security traditionally has painted on sidewalks around the plants to mark where strike pickets cannot cross.

Within an hour of the rally’s end, the leadership of the International Association of Machinists (IAM) had heard enough from the rank-and-file to make a decision.

“It’s official,” Mark Blondin, IAM national aerospace coordinator, said in a phone interview. “We are recommending to reject the contract and to vote to strike.”

Union members will vote on the contract offer Wednesday. If two-thirds of voters heed Blondin’s recommendation, a strike will begin at midnight.

Some 26,000 of the affected workers are in the Puget Sound region, with an additional 1,500 in Portland and about 800 at the defense-aircraft modification plant in Wichita, Kan.

If the IAM strikes, Boeing engineers and other non-Machinists would continue to work. But all production would shut down at the jet-assembly plants in Everett and Renton and at the parts plants in Auburn and Frederickson. Most fabrication and production work at the military-aircraft and technology-research centers in Seattle also would cease.

Assembly work on the already much-delayed 787 Dreamliner program would be suspended for as long as a strike lasts. The first Dreamliner presently is due to fly in November.

At a news conference at the SeaTac Doubletree Hotel, the venue for the intensive talks of the past week, IAM District President Tom Wroblewski said he remains ready to talk right up to the contract deadline Wednesday. He said he’d welcome the help of the federal mediator.

“We stand ready to meet at any time,” Wroblewski said.

But Boeing spokesman Tim Healy said the offer put to the union Thursday is final. Boeing is willing to clarify and explain its terms, but won’t improve them before the strike vote.

Healy said the company still hopes for a positive vote after union members study the contract carefully and use a benefits calculator on the company’s Web site to work out the precise financial impact on each individual’s family circumstances.

“We think they will see the value,” Healy said.

Under the current contract, Machinists earn an average base pay of $54,000 a year. With overtime, the average is $65,000.

At the end of the three-year contract, the average base pay would increase to $65,000, and with overtime the figure would be $77,000, according to Boeing.

Over the three years, Boeing estimates that an average Machinist would receive $34,000 more in total pay, compared with the current contract.

Wroblewski cited a long list of reasons for rejecting the offer, including the lack of job-security commitments, increases in medical-plan costs, and pay and pension increases that didn’t meet union members’ expectations.

Union officials had gone over the contract offer with a fine-tooth comb. A document on the medical-plan deficiencies listed details such as no increase in coverage for prescription lenses, and a reduction in dental coverage from three annual cleanings to two.

Machinists particularly upset with the contract offer included relatively new hires, who are low on the company wage ladder. The proposed contract would give them smaller percentage increases than more senior workers.

Scott Shampine, an electrician on the 737 line in Renton hired 18 months ago, said he has gross pay with overtime of about $36,000.

The compensation calculator on the Boeing Web site shows Shampine’s gross pay with overtime and bonuses going up to $42,000 the first year and to $47,000 at the end of the final year.

But Shampine found the details confusing. He said he believes the offer gives him a raise of just 6 cents an hour in the initial months. He said he doesn’t trust the company calculator’s result.

Boeing spokesman Healy said Shampine has misinterpreted details of the compensation offer. He said Shampine would receive a $1.14 raise immediately.

Shampine said he plans to reject the contract and vote to strike Wednesday.

Separately, the IAM filed an unfair-labor-practice complaint Thursday with the National Labor Relations Board, accusing Boeing of violating labor law during negotiations by “going around the union and trying to bargain directly with our members,” Blondin said.

The union alleges Boeing violated the federal requirement for employers to bargain exclusively with designated union representatives. It cited as evidence an e-mail from a Boeing communications person obtained by the union that outlined company efforts to ask individual employees their views on specific contract proposals.

Healy said the e-mail merely referred to a legitimate company effort to get employee feedback.